Let us consider the parton-to-hadron transition first. One way to add hadronisation effects to our
\(\text{NLO} +\text{NLL}  ^\prime \)  results is to perform a field-theoretical analysis, based on non-perturbative matrix elements.
However, the jet structure may not only be significantly affected by hadronisation but also by the
UE. The underlying event, unlike hadronisation, should not be seen as a non-perturbative
correction to our \(Zj\)  matrix elements, but rather as independent semi-hard processes, contributing
with additional final-state partons that ultimately hadronise. Therefore, the UE cannot be
straightforwardly included into the resummation framework beyond the simple model of uniform
radiation [1]}, [2]}. Moreover, hadronisation may lead to non-trivial
clustering of partons from different processes, i.e. the hard scattering and the UE,
into final-state hadrons. Therefore, we prefer to rely
on dynamical non-perturbative models as implemented in the PYTHIA, HERWIG and SHERPA MC event
generators [3]}. Each of these programs is using its own default combination of
non-perturbative models for hadronisation and UE. More precisely, in both the PYTHIA and SHERPA frameworks the UE is described by the Poisson-based Sjöstrand–Zijl model presented
in [4]}, [5]}, [6]} whereas in HERWIG the UE is
simulated based on the eikonal-model for soft emissions [7]}, [8]}. The hadronisation
effects are simulated according to the Lund string model [9]}, [10]} in PYTHIA and according to cluster-fragmentation models both in HERWIG [11]}, [12]} and
SHERPA [13]}.
